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H. Aziz, P. Biro, S. Gaspers, R. de Haan, N. Mattei, B. Rastegari:
"Stable Matching with Uncertain Linear Preferences";
Vortrag: International Symposium on Algorithmic Game Theory, Liverpool, United Kingdom; 19.09.2016 - 21.09.2016; in: "Proceedings of the 9th International Symposium on Algorithmic Game Theory - SAGT 2016", (2016), ISBN: 978-3-662-53353-6; S. 195 - 206.

We consider the two-sided stable matching setting in which there may be uncertainty about the agents´ preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model - in which for each agent, there is a probability distribution over linear preferences, (2) compact indifference model - for each agent, a weak preference order is specified and each linear order compatible with the weak order is equally likely and (3) joint probability model - there is a lottery over preference profiles. For each of the models, we study the computational complexity of computing the stability probability of a given matching as well as finding a matching with the highest probability of being stable. We also examine more restricted problems such as deciding whether a certainly stable matching exists. We find a rich complexity landscape for these problems, indicating that the form uncertainty takes is significant.

http://publik.tuwien.ac.at/files/publik_256475.pdf